The aliasing problem in lattice field theory

TL;DR

This paper discusses the aliasing problem in lattice quantum field theory caused by high-momentum components masquerading as low-momentum ones, and proposes a strategy to eliminate these artifacts for more accurate calculations.

Contribution

It introduces a general method to eliminate aliasing artifacts in lattice quantum field theory calculations, improving the accuracy of physical predictions.

Findings

Aliasing causes significant distortions in lattice calculations.

A proposed strategy effectively reduces aliasing artifacts.

Enhances the reliability of lattice quantum field theory computations.

Abstract

The intrinsically nonlinear nature of quantum field theory provides a fundamental complication for lattice calculations, when the physical implications of the subtleties of Fourier theory are taken into account. Even though the fundamental fields are constrained to the first Brillouin zone, Fourier theory tells us that the high-momentum components of products of these fields "bleed into" neighbouring Brillouin zones, where they "alias" (or "masquerade") as low-momentum contributions, violating the conservation of energy and momentum, and fundamentally distorting calculations. In this paper I offer a general strategy for eliminating the artefacts of aliasing in practical calculations.